In a busy first half, the best efforts fell to Alex Gilliead, whose fierce first-time drive was tipped over by Dean Henderson, and Jon Nolan, who was clean through on goal but fired straight at Doyle.
Shrewsbury stepped up a gear after the restart and came close to opening the scoring on 55 minutes when Rodman ran at the opposition defence and rifled just over the bar from 25 yards.
Despite going a man down, Paul Hurst's charges continued to press and enjoyed several more opportunities to open the scoring, but ultimately they could not break through the Bantams' defence and the points ended up being shared between the two sides.
The result means that Shrewsbury are now four points off the top two of Wigan Athletic and Blackburn Rovers, while Bradford sit 12th in the standings, eight points adrift of the playoffs.
BRADFORD CITY (4-4-1-1): Doyle; Tony, Kilgallon, Knight-Percival, Warnock (Chicksen 73'); Gilliead, Dieng, Guy, Robinson; Brunker (Patrick 76'), Wyke
SHREWSBURY TOWN (4-1-4-1): Henderson; Bolton, Nsiala, Sadler, Beckles; B. Morris (C. Morris 63'); Whalley, Nolan, Godfrey, Rodman; Payne (John-Lewis 81')body check tags ::